Mine are more than 3/4" and less than 1". They look fine to me. I'm not sure what else to tell you!

Many mid to hi end brands offer 1" doors. I have them in Quality Custom Cabinetry, Mountaineer, Kropp, and RichMaid, can think of at least a dozen more that have them.
The look for insets has more to do with the door style. I'm putting in a display with 1" doors in QCCI only because the framing bead looks better with a 1" than it does with a 3/4"
First pic below.

Some brands (hi end) also offer 1" frames (standard for inset in QCCI) Where that shows the best is if the door is held back from the face frame a little- often with an extra edge detail around the opening. This is usually only done for a feature section or cabinet- can get busy for an entire kitchen. Second pic below- 1" thick door, inset with cove detail on edge--definitely NOT shaker :)

Maybe I am missing something.... but on an inset drawer, how could you even tell what the thickness was (unless you opened the drawer)?

Only by the framing bead,i.e.on the white door above the cove would be shallower and narrower if the door were 3/4

If you like paying for complete overkill, go ahead. It has zero to do with actual functionality. It IS a fabulous look though. Most people would rather put that money to doing all drawers in the kitchen. Or, if you're one of the lucky few that can do the 100K+ kitchen remodel with the 1" thick with drawers and all of the bells and whistles without having to worry about the choices, then don't sweat it at all and proceed. That's not most of us though, and we probably want to live vicariously through your remodel. :P